$\dfrac{ -3j - 8k }{ 9 } = \dfrac{ -j - 5l }{ 2 }$ Solve for $j$.
Explanation: Multiply both sides by the left denominator. $\dfrac{ -3j - 8k }{ {9} } = \dfrac{ -j - 5l }{ 2 }$ ${9} \cdot \dfrac{ -3j - 8k }{ {9} } = {9} \cdot \dfrac{ -j - 5l }{ 2 }$ $-3j - 8k = {9} \cdot \dfrac { -j - 5l }{ 2 }$ Multiply both sides by the right denominator. $-3j - 8k = 9 \cdot \dfrac{ -j - 5l }{ {2} }$ ${2} \cdot \left( -3j - 8k \right) = {2} \cdot 9 \cdot \dfrac{ -j - 5l }{ {2} }$ ${2} \cdot \left( -3j - 8k \right) = 9 \cdot \left( -j - 5l \right)$ Distribute both sides ${2} \cdot \left( -3j - 8k \right) = {9} \cdot \left( -j - 5l \right)$ $-{6}j - {16}k = -{9}j - {45}l$ Combine $j$ terms on the left. $-{6j} - 16k = -{9j} - 45l$ ${3j} - 16k = -45l$ Move the $k$ term to the right. $3j - {16k} = -45l$ $3j = -45l + {16k}$ Isolate $j$ by dividing both sides by its coefficient. ${3}j = -45l + 16k$ $j = \dfrac{ -45l + 16k }{ {3} }$